Question

find the value of x that makes quadrilateral pqrs a parallelogram.
(image of quadrilateral pqrs with side rq labeled 2x and side sp labeled x + 7, with arrows indicating those sides are congruent)
\\( x = \square \\)
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Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite sides are equal in length. So, \( RQ = SP \).

Step2: Set up the equation

Given \( RQ = 2x \) and \( SP = x + 7 \), we set \( 2x = x + 7 \).

Step3: Solve for x

Subtract \( x \) from both sides: \( 2x - x = x + 7 - x \), which simplifies to \( x = 7 \).

Answer:

\( x = 7 \)